High backscattering waveguides

ABSTRACT

A high backscattering optical fiber comprising a perturbed segment in which the perturbed segment reflects a relative power such that the optical fiber has an effective index of n eff , a numerical aperture of NA, a scatter of R p→r   (fiber) , a total transmission loss of α fiber , an in-band range greater than one nanometer (1 nm), a center wavelength (λ 0 ) of the in-band range (wherein 950 nm&lt;λ 0 &lt;1700 nm), and a figure of merit (FOM) in the in-band range. The FOM&gt;1, with the FOM being defined as: 
     
       
         
           
             FOM 
             = 
             
               
                 
                   R 
                   
                     p 
                     → 
                     r 
                   
                   
                     ( 
                     fiber 
                     ) 
                   
                 
                 
                   
                     
                       α 
                       fiber 
                     
                     ⁡ 
                     
                       ( 
                       
                         NA 
                         
                           2 
                           ⁢ 
                           
                             n 
                             eff 
                           
                         
                       
                       ) 
                     
                   
                   2 
                 
               
               .

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 15/15/468,159, filed 2017 Mar. 24, by Kremp, etal., having the title “High Backscattering Waveguides,” which is adivisional application of U.S. patent application Ser. No. 15/175,656,filed 2016 Jun. 7, by Kremp, et al., having the title “HighBackscattering Waveguides,” which claims the benefit of U.S. provisionalpatent application Ser. No. 62/172,336, filed 2015 Jun. 8, by Kremp etal., having the title “High Backscattering Fiber,” all of which areincorporated herein by reference in their entireties.

BACKGROUND Field of the Disclosure

The present disclosure relates generally to waveguides and, moreparticularly, to high backscattering waveguides.

Description of Related Art

Various optical sensing methods rely on measurements of backscatteredsignals from a waveguide to determine physical quantities such astemperature or strain along the waveguide. For example, in opticalfrequency domain reflectometry (OFDR) or optical time domainreflectometry (OTDR), temperatures or strains along an optical fiber canbe measured based on backscattering. To improve the accuracy andrepetition rates of these measurements, there are ongoing efforts toimprove the signal-to-noise ratio (SNR) of the backscattered signal.

SUMMARY

The present disclosure provides high backscattering waveguides (e.g.,optical fibers) and sensors employing high backscattering opticalfibers. Briefly described, one embodiment comprises a highbackscattering fiber that reflects a relative power that is more thanthree (3) decibels (dB) above the Rayleigh scattering. For someembodiments, the high backscattering fiber also exhibits a coupling lossof less than 0.5 dB.

Other systems, devices, methods, features, and advantages will be orbecome apparent to one with skill in the art upon examination of thefollowing drawings and detailed description. It is intended that allsuch additional systems, methods, features, and advantages be includedwithin this description, be within the scope of the present disclosure,and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the disclosure can be better understood with referenceto the following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIGS. 1A and 1B are graphs showing the reflectivity for one embodimentin which the integration length is one (1) millimeter (mm) in a 119.5centimeter (cm) long fiber section with a design level of −80 decibel(dB) backscatter per 1 mm (1/mm) in a wavelength range of 1550±7.5nanometers (nm). The shortest integration length, for which thebackscatter enhancement persists over the full measurement (e.g., OFDRor OTDR) bandwidth, is an approximate lower bound for the achievablespatial resolution of the measurement system.

FIGS. 2A and 2B are graphs showing the reflectivity for one embodimentin which the integration length is 30 mm in a 119.5 cm-long fibersection with a design level of −80 dB backscatter per 1 mm in awavelength range of 1550±7.5 nm.

FIGS. 3A and 3B are graphs showing the reflectivity for one embodimentin which the integration length is approximately 0.3 mm (more precisely,0.299 mm) in a 29.4 cm-long fiber section with a design level of −60 dBbackscatter per 1 mm in a wavelength range of 1550±7.5 nm.

FIGS. 4A and 4B are graphs showing reflectivity for one embodiment inwhich the integration length is 1 mm in a 29.4 cm-long fiber sectionwith a design level of −60 dB backscatter per 1 mm in a wavelength rangeof 1550±7.5 nm.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Rayleigh scattering (both forward scattering and backscattering) occursin all optical fibers and is a well-documented phenomenon. Typicaloptical fibers exhibit random refractive index fluctuations at scales oftens of nanometers. These fluctuations are responsible for so-calledRayleigh scattering, which arises from thermal fluctuations that arefrozen into the fiber during the draw process. Their presence gives riseto both a back scattered signal for core-guided light, which is usefulfor many sensing applications, as well as light scattering to non-guidedlight, which results in losses for transmitted light. The Rayleighscattering is usually very broadband and has a relatively low intensitythat is approximately (in the limit of very small scattering centers)proportional to the inverse fourth power (λ⁻⁴) of the wavelength (λ).

Physical quantities such as temperature and strain along an opticalfiber are measurable using optical sensing methods that measure Rayleighbackscattering, such as optical frequency domain reflectometry (OFDR)and optical time domain reflectometry (OTDR). As in most measurements,high signal-to-noise ratio (SNR) provides greater accuracy and higherrepetition rates.

One way of increasing the SNR of the backscattered signal is byincreasing core dopant levels to enhance density fluctuations that giverise to Rayleigh scattering and increase the measurable backscattering.However, increasing core dopant levels increases the overall loss of thefiber, thereby limiting the achievable SNR. Additionally, increaseddopant levels reduce design flexibility that is oftentimes required forcomplex fiber profiles, such as multi-core fibers, low birefringencefibers, fibers with polarization maintaining properties and otherdemanding designs. Because these complex designs require precise controlof modal effective index, core placement, symmetry, eccentricity, andovality of the fiber core, controlling backscatter by increasing dopantlevels is difficult and sometimes results in optical signals beingtransported over the same lossy waveguide that is used for sensing thebackscatter.

High backscattering optical fibers and the sensors with highbackscattering fibers, as disclosed herein, provide solutions thatincrease backscatter without significantly affecting other properties ofthe waveguide. This is accomplished by altering or modifying therefractive index by applying an appropriate spatial pattern that createsa refractive index perturbation, which: (a) causes a reflectivity thatis greater than three (3) or preferably greater than ten (10) decibels(dB) above Rayleigh scattering within one or more ranges of desiredwavelengths (in-band) (for both single and multiple wavelength windows);but (b) maintains signal integrity and exhibits a coupling loss with astandard single-mode or multimode fiber of less than 0.5 dB, orpreferably less than 0.2 dB. In other words, by applying an appropriatespatial pattern, such as a longitudinal perturbation induced byultraviolet (UV) light in the refractive index of the core, the highbackscattering optical fiber can attain a backscattered signal (within adesired range or multiple desired ranges of wavelengths (in-band) and ata desired longitudinal resolution length) that is at least 3 dB, orpreferably at least 10 dB, above the Rayleigh backscatter observedoutside of the desired range (out-of-band) at the desired longitudinalresolution length. As shown in greater detail below, the ratio ofoptical backscatter to the power that is lost in transmission (averagedover the in-band) is more than two (2) times, preferably ten (10) timesthe value measured for standard single-mode fibers that rely only onRayleigh backscattering.

One way of modifying the refractive index profile is by subjecting theoptical fiber waveguide to actinic radiation. Actinic radiation caninclude UV, IR or other electromagnetic radiation. When subjected tosuch actinic radiation, the refractive index of the optical waveguide ismodified. Such modifications can increase the back scattering of lightguided by the waveguide. The spectrum of the enhanced backscatterdepends on the spatial structure of the refractive index modification.For instance, exposure to a modulated or unmodulated UV beam can cause abroadband increase of the backscatter. In contrast, a narrowbandincrease of the backscatter requires that the product ofphotosensitivity and dosage (time integral of the intensity) of theactinic radiation varies along the waveguide. More precisely, if thespatial Fourier transform (along a certain length l in directionparallel to the waveguide and in the neighborhood of the longitudinalposition z) of this product has a significant components at the periodλ/(2n_(eff)), which is half the wavelength of the guided light (i.e.,free space wavelength λ divided by double the effective index of thewaveguide), then the guided light will experience increased backreflection over what such light would experience in an unexposedwaveguide at this position z. For instance, if a UV beam with awavelength of 200 nm is directed onto a fiber waveguide such that theaccumulated dosage of the UV beam varies along the waveguide axis with aperiod of about 500 nm, then the resulting refractive index modificationwould result in increased scatter for guided light with a wavelengthnear 1000 nm. For a silica waveguide, such a wavelength would correspondto approximately a 1500 nm vacuum wavelength. Spatial variations may beimposed on the actinic beam through various optical techniques, e.g.,interference patterns from phase masks, point-by-point inscription,diffuse scattering elements, and femtosecond systems.

Having generally described a high backscattering fiber that does notsignificantly affect other waveguide properties, specific embodiments ofhigh backscattering fibers, along with their design criteria, areexplained in greater detail below, making reference to the drawings toillustrate the achievable results of such a high backscattering fiber.While several embodiments are described herein, there is no intent tolimit the disclosure to the embodiment or embodiments disclosed herein.On the contrary, the intent is to cover all alternatives, modifications,and equivalents.

For purposes of illustration, in one embodiment, a high backscatteringfiber is described, which is capable of propagating a signal (p) andcounter-propagating a reflected signal (r). The longitudinal axis of thefiber is designated as z, while the transverse axes, which areperpendicular to the waveguide axis, are designated as x and y.

Without loss of generality, we write the total refractive index profilen^((total))x,y,z) of the high backscattering fiber as the sum of az-independent term n_(x,y)(x,y) and a z-dependent termΔn^((total))(x,y,z):n ^((total))(x,y,z)=n(x,y)+Δn ^((total))(x,y,z)  (1)Since any perturbation of the refractive index profile of the fiber addsto any Rayleigh scattering that already exists in the fiber, the termΔn^((total))(x,y,z) in Eq. (1) is the sum of the refractive indexfluctuation Δn^((Rayleigh))(x,y,z) that gives rise to Rayleighscattering, and an additional refractive index perturbation Δn(x,y,z):Δn ^((total))(x,y,z)=Δn ^((Rayleigh))(x,y,z)+n(x,y,z).  (2)Those having skill in the art will appreciate that the z-dependentperturbation term Δn(x,y,z) in Eq. (2) can be applied independently ofother fiber fabrication steps, such as during or after fiber draw. Inparticular, certain sections of the fiber can have Δn=0.

To keep the mathematical modeling as simple as possible, we assume thatthe perturbation term Δn in Eq. (2) can be written as the product of twoterms that separately depend on the transverse coordinates (x,y) and onthe longitudinal position z:Δn(x,y,z)=Δn _(x,y)(x,y).Δn _(z)(z).  (3)

In other words, we assume that the (x,y)-dependence of the refractiveindex perturbation term does not change along z. If this assumption isnot valid, e.g., in presence of fiber fabrication inaccuracies ortapering, a high backscattering fiber is still possible, but themathematical modeling (see Eqs. (5/6) below) would be more involved.

Combining Eqs. (1-3), we obtain the total refractive index distributionn ^((total))(x,y,z)=n _(x,y)(x,y)+Δn ^((Rayleigh))(x,y,z)+Δn_(x,y)(x,y)Δn _(z)(z).  (4)

With E_(p)(x,y) and n_(eff,p), respectively, we denote an eigenmode anda corresponding effective index of the waveguide that is described bythe z-independent refractive index profile n_(x,y)(x,y) in Eq. (1). Anexample is the fundamental mode p=LP_(0,1) of a cylindrical opticalfiber. To further simplify the following mathematical description, weassume that the presence of the z-dependent refractive index termΔn^((total))(x,y,z) does not significantly change the eigenmodes andeffective indices. If this assumption is not valid, e.g., in the case ofstrong refractive index perturbations along a short section of thewaveguide, a high backscattering fiber is still possible, but themathematical modeling (see Eqs. (5/6) below) would be more involved.

With R_(p→r)(λ,z,l), we denote the relative amount of power that isbeing reflected per unit length from fiber mode E_(p) to acounter-propagating mode E_(r) at wavelength λ due to the additionalrefractive index perturbation Δn(x,y,z) in a section of length l atposition z. R_(p→r)(λ,z,l) has the unit 1/m, so it is actually areflectivity density, but, for convenience, we sometimes refer to it asthe “relative reflected power,” “reflectivity,” or “enhancedbackscatter,” respectively. If the chosen integration length l issufficiently short or if Δn(x,y,z) in Eq. (3) is sufficiently weak, thenmultipath interference (MPI) effects along the length l can beneglected, and the relative reflected power R_(p→r)(λ,z,l) from a solesection of length l is approximately given by:

$\begin{matrix}{{{R_{p->r}( {\lambda,z,l} )} \approx {\frac{1}{l}{{\mu_{p,r}\frac{2\pi}{\lambda}{\int_{z - \frac{l}{2}}^{z + \frac{l}{2}}{\Delta\;{n_{z}( z^{\prime} )}e^{i\; 2\pi\; z^{\prime}\frac{n_{{eff},p} + n_{{eff},r}}{\lambda}}{dz}^{\prime}}}}}^{2}}},} & (5)\end{matrix}$with n_(eff,p) representing the effective index of the forwardpropagating mode E_(p), and n_(eff,r) representing the effective indexof the backward propagating mode E_(r). Numerically, the integral in Eq.(5) can be evaluated efficiently using a Fast Fourier Transform (FFT)algorithm. The modal overlap coefficient μ_(p,r) in Eq. (5) is definedas

$\begin{matrix}{{\mu_{p,r}:=\frac{\int{\int_{- \infty}^{\infty}{{E_{p}( {x,y} )}\Delta\;{n_{x,y}( {x,y} )}{E_{r}^{*}( {x,y} )}{dxdy}}}}{\sqrt{\int{\int_{- \infty}^{\infty}{{{E_{p}( {x,y} )}}^{2}{dxdy}}}}\sqrt{\int{\int_{- \infty}^{\infty}{{{E_{r}( {x,y} )}}^{2}{dxdy}}}}}},} & (6)\end{matrix}$where the asterisk symbol (*) represents a complex conjugate. This modaloverlap coefficient μ_(p,r) summarizes the mode-coupling-relatedtransverse properties of the two considered modes E_(p) and E_(r) andthe refractive index distribution. R_(p→r)(λ,z,l) can be measured, e.g.,using a commercially available OFDR system (some OFDR systems refer to las an integration width).

With R_(p→r) ^((Rayleigh))(μ,z), we denote the Rayleigh backscatter fromfiber mode E_(p) to a counter-propagating mode E_(r) at wavelength λ andposition z, which is well known to add incoherently and therefore isindependent of the integration length l. Assuming that the Rayleigh andenhanced backscatter add incoherently as well, the total backscatter ofthe fiber is approximately given by:R _(p→r) ^((fiber))(λ,z,l)≈R _(p→r) ^((Rayleigh))(λ,z)+R_(p→r)(λ,z,l).  (7)

Possible constraints on the enhanced backscatter reflectivityR_(p→r)(λ,z,l) are that, similar to the Rayleigh scatter R_(p→r)^((Rayleigh))(λ, z), it should (a) be present at all positions z alongthe waveguide in order to avoid blind spots, and/or that R_(p→r)(λ,z,l)should (b) be approximately independent of the integration length l,i.e., the backscatter intensity should scale linearly with theconsidered integration length l, and/or that, unlike the broadbandRayleigh scatter R_(p→r) ^((Rayleigh))(λ, z), the enhanced backscatterR_(p→r)(λ,z,l) should (c) preferably exist only in a well controlledrange of wavelengths (in-band), which may be equal to the bandwidth ofthe interrogation scheme (OTDR, OFDR, etc.), to keep the required dosageof the actinic radiation and the induced additional transmission lossfor the guided light as low as possible. For any given modal overlapcoefficient μp,r and target function R_(p→r)(λ,z,l), a longitudinalrefractive index distribution Δn_(z)(z) that satisfies all or some ofthese conditions may be found by solving the approximative Eq. (5) forΔn_(z)(z), e.g., using an inverse Fourier transform, and using asuitable assumption for the phase of the integral on the right hand sidein Eq. (5). If Δn(x,y,z) in Eq. (3) is not sufficiently weak, multipathinterference (MPI) effects cannot be neglected and Eq. (5) may not beaccurate enough for practical purposes. In this case, the moretime-consuming inverse scattering problem that relates the reflected andincident waves in the considered section of the waveguide in theframework of Maxwell's equations needs to be solved to find Δn_(z)(z).

The enhancement in scatter of the present invention may also beunderstood from the well-known dependencies of back scattering andtransmission loss in optical fibers. For example, others (such asNakazawa (in JOSA73(1983), 1175-1180) and Personick (in Bell Tech J.56(1977), 355-366)) have shown that the power fraction lost intransmission per unit length due to Rayleigh scattering, is given by theRayleigh scattering coefficient α_(Rayleigh)(λ,z), which is usuallyproportional to λ⁻⁴. It is also known that the core guided, backscattering signal from a given length of fiber is proportional toα_(Rayleigh) and to the fiber recapture fraction, which is proportionalto the square of the fiber numerical aperture NA². In the case thatE_(p) is the fundamental mode of the fiber, and E_(r) is thecounterpropagating fundamental mode, we have:

$\begin{matrix}{{{R_{p->r}^{({Rayleigh})}( {\lambda,z} )} = {{\alpha_{Rayleigh}( {\lambda,z} )}( \frac{NA}{2n_{eff}} )^{2}}},} & (8)\end{matrix}$where R_(p→r) ^((Rayleigh)) is the relative fraction of light backscattered per unit length (from fiber fundamental mode E_(p) tocounter-propagating fundamental mode E_(r)), and n_(eff) is theeffective index of the mode. Therefore, any fiber design that increasesthe backscattering due to an increase in Rayleigh scattering coefficientwill also increase the transmission loss (in fundamental mode E_(r)). Inrealistic fibers, the loss due to Rayleigh scattering is accompanied byother transmission losses. That is, the total fraction of power lost perunit length is:α_(fiber)=α_(Rayleigh)+α_(non-Rayleigh).  (9)Here, α_(non-Rayleigh) is the fraction of power lost in transmission tomechanisms other than Rayleigh scattering, such as UV or IR absorptionor Mie scattering. In general, a figure of merit may then be derived forany fiber by considering a given length of the fiber and measuring thelight that is back scattered (from fiber fundamental mode E_(p) tocounter-propagating fundamental mode E_(r)) and the light that is lostin transmission (in fiber mode E_(p)) through that length. To normalizeout the effect of the NA, the following figure of merit (FOM) may becomputed from these measured quantities:

$\begin{matrix}{{FOM} = {\frac{R_{p->r}^{({fiber})}}{{\alpha_{fiber}( \frac{NA}{2n_{eff}} )}^{2}}.}} & (10)\end{matrix}$

The light that is backscattered, R_(p→r) ^((fiber)), may be measuredusing for instance optical frequency or time domain reflectometry. Thetotal transmission loss α_(fiber) may be measured with standard fiberloss cut back measurements. For an ideal fiber with only Rayleighscattering, we have FOM=1. For non ideal fibers with loss mechanismsother than Rayleigh scattering, we have FOM<1. The invention of thispatent in general has FOM>1, and preferably FOM>2 or larger for at leastsome range of wavelengths λ.

Preferably, for some embodiments, R_(p→r)(λ,z,l) is consideredsufficiently strong if it is more than 10 dB above the native Rayleighscattering of the fiber. In the case of standard single mode fiber, thenative Rayleigh scattering level is approximately R_(p→r)^((Rayleigh))≈6·10³¹ ¹¹/mm. Applying the decadic logarithm andmultiplying with a factor of 10, we obtain 10 log₁₀(6·10⁻¹¹)=−102.22.Since this is the same procedure used for the unit decibel (dB), it iscommon to denote this value as −102 “dB/mm” (or, equivalently, −72“dB/m”, due to 6·10⁻¹¹/mm=6·10⁻⁸/m and 10 log₁₀(6·10⁻⁸)=−72.22).

Regarding the total length L of the fiber, which can be of the order ofmeters (m) to kilometers (km), MPI can typically be neglected ifR_(p→r)(λ,z,L)·L<0.01 for all λ, i.e., for total backscattering levelsbelow −20 dB.

Those having skill in the art will appreciate that the ability to tailorΔn_(z)(z) in Eq. (5) results in a corresponding ability to tailor theamount of backscattering without significantly affecting other signaltransmission and reflection properties, such as e.g., loss,nonlinearity, or mode field diameter.

To be clear, the tailored perturbation Δn(x,y,z) should meet severalrequirements with respect to its transverse properties, longitudinalproperties, and spectral properties. For example, Δn(x,y,z) shouldinduce only a minimal amount of loss for the modes E_(p) and E_(r) inwhich an interrogation signal is propagating in forward and backwarddirection. Also, the mode E_(r) should recapture a maximum fraction ofthe additional backscattering. Additionally, the backscatter from theseindex perturbations should be spectrally sufficiently wide to cover thefull wavelength range of the interrogation scheme (e.g., OFDR or OTDR)used to measure backscatter, even in the presence of the highestpossible variations in temperature or strain that this backscatteringfiber is intended to be able to measure.

Some embodiments further comprise an optical pump that operates at awavelength that is outside of the wavelength range that is affected bythe index perturbation. For example, if the index perturbation increasesbackscatter in a wavelength range that is between 1542.5 nm and 1557.5nm, then the optical pump has a wavelength that is outside of thatrange. Such a pump signal may however produce gain within the increasedback scatter range.

Spectral broadening of the backscatter signal to spectral regions thatare not part of the interrogation scheme should be avoided becauseadditional backscatter from those spectral regions does not increase theSNR but, instead, can have detrimental effects such as increasedabsorption or overall signal or optical pump attenuation in the fiber.Furthermore, to avoid unwanted blind spots along the fiber, there shouldbe a sufficiently strong backscatter signal in the interrogation scanrange from every fiber section that is longer than or equal to theintended spatial resolution of the interrogation scheme. Therefore, theshortest integration length, for which the backscatter enhancementpersists over the full measurement (e.g., OFDR or OTDR) bandwidth, is anapproximate lower bound for the achievable spatial resolution of themeasurement system. Preferably, the backscatter will be greater than 10dB above the Rayleigh scattering level to be considered sufficient foradequate interrogation. All of these properties can be ascertained bythose having ordinary skill in the art from Eqs. (1-6) and theembodiments described herein.

With Eqs. (1-6) and the desired properties of a preferred embodiment ofthe high backscattering fiber in mind, one example of an interferometricmeasurement of a device under test (DUT) is explained for an OFDRinterrogator with a fiber of group index n_(group)=1.45 and a scan rangeΔλ=15 nanometers (nm) from 1542.5 nm to 1557.5 nm. Typically, such OFDRmethods measure a wide spectral range (e.g., 10 nm or more), and theimpulse response in the time domain can be computed by the Fouriertransform of the measured spectrum. If the original spectral data isproportional to the complex-valued reflection amplitude of the DUT, thenthe modulus squared of its impulse response is proportional to thereflected power in the time domain. If MPI and group velocity dispersion(i.e., the dependence of the group velocity on the wavelength) arenegligible in the measured scan range, then this relative reflectedpower at time (t) is proportional to the reflectivity (per unit length,see the definition in Eq. (5)) of the DUT at position (z), such that:

$\begin{matrix}{{z = {{t\;\frac{v_{group}}{2}} = {t\;\frac{c_{0}}{2n_{group}}}}},} & (11)\end{matrix}$where v_(group) and n_(group) represent the average group velocity andgroup index in the scan range, co represents the speed of light invacuum, and the factor of 2 in the denominator accounts for the factthat the light travels to position z and back, thereby doubling thedistance traversed. Thus, according to the Nyquist sampling theorem, aspatial resolution of 55.2 micrometers (μm) is possible in our example:

$\begin{matrix}{{\Delta\; z} = {{{\frac{c_{0}}{2n_{group}}\Delta\; t} \approx \frac{\lambda^{2}}{2n_{group}\Delta\;\lambda}} = {\frac{( {1550\mspace{14mu}{nm}} )^{2}}{{2 \cdot 1.45 \cdot 15}\mspace{14mu}{nm}} = {55.2\mspace{14mu}{{\mu m}.}}}}} & (12)\end{matrix}$The OFDR interrogator can achieve this resolution for a relatively shortsensor length (e.g., several meters). The Nyquist sampling theoremsimilarly implies that longer sensing lengths require more (spectrallycloser) spectral measurements in the given scan range and, therefore,longer scan times. This increases the sensitivity to any kind of fastvariations, such as vibrations. To keep the measurement time andvibration sensitivity constant, the product of spatial resolution andsensing length should remain constant. In other words, longer sensinglengths can be achieved at the cost of coarser spatial resolution orincreased sensitivity to vibrations.

FIGS. 1-4 show examples in the case p=r=LP₀₁, i.e., both the propagatingsignal (p) and the counter-propagating reflected signal (r) arepropagating in the fundamental mode (LP₀₁) of a single-mode opticalfiber. Hence, R_(p→r) in Eq. (5) is designated as R_(LP) _(01→) _(LP) ₀₁. FIGS. 1 and 2 show a longer sensing length L=119.5 cm as compared to ashorter sensing length L=29.4 cm in FIGS. 3 and 4.

FIGS. 1A and 1B are graphs showing a plot of the reflectivity inlogarithmic unit (10·log₁₀(R_(LP) _(01→) _(LP) ₀₁ )) from Eq. (5) withan integration length l=1 mm for one embodiment in a 119.5 cm-long fibersection with a backscatter design level of −80 dB/mm in a wavelengthrange of 1550±7.5 nm, i.e.,

$\begin{matrix}{{{R_{{LP}_{01}->{LP}_{01}}( {\lambda,z} )} \approx \frac{10^{- 8}}{mm}},{\lambda \in \lbrack {{1542.5\mspace{14mu}{nm}},{1557.5\mspace{14mu}{nm}}} \rbrack},{0 \leq z \leq {1.195\mspace{14mu}{m.}}}} & (13)\end{matrix}$

Specifically, FIG. 1A plots, in three dimensions (3D), the reflectivity(in unit dB/mm) as a function of wavelength (λ) and z-position along thefiber (in meters (m)); using an integration length l=1 mm. The shortestintegration length for which the backscatter enhancement persists overthe full measurement (e.g., OFDR or OTDR) bandwidth is an approximatelower bound for the achievable spatial resolution of the measurement.FIG. 1B shows the same result in a two-dimensional (2D) plot. FIGS. 2Aand 2B are graphs showing reflectivity with an integration length l=30mm, with all other parameters being equal to those of FIGS. 1A and 1B,respectively.

FIGS. 3A and 3B are graphs showing a plot of reflectivity with anintegration length of approximately 0.3 mm (more precisely, 0.299 mm) ina 29.4 cm-long fiber section with a backscatter design level of −60dB/mm in a wavelength range of 1550±7.5 nm, i.e.,

$\begin{matrix}{{{R_{{LP}_{01}->{LP}_{01}}( {\lambda,z} )} \approx \frac{10^{- 6}}{mm}},{\lambda \in \lbrack {{1542.5\mspace{14mu}{nm}},{1557.5\mspace{14mu}{nm}}} \rbrack},{0 \leq z \leq {29.4\mspace{14mu}{{cm}.}}}} & (14)\end{matrix}$

Specifically, FIG. 3A plots in 3D the reflectivity (in dB/mm) as afunction of A and z-position along the fiber, using an integrationlength of 0.299 mm. FIG. 3B shows the same result in a 2D plot. FIGS. 4Aand 4B are graphs showing reflectivity for one embodiment in which theintegration length is 1 mm, with all other parameters being equal tothose of FIGS. 3A and 3B, respectively.

The setup for FIGS. 1A, 1B, 2A, and 2B includes six (6) individual 20cm-long sections with an overlap of 1 mm between each section, therebyresulting in a fiber of length L=119.5 cm. To achieve the intendedbackscatter enhancement, the refractive index perturbation Δn_(z)(z)(see Eq. (3)) does not need to be periodic or quasi-periodic with thisperiod of 20 cm or 19.9 cm, respectively. In the core of the fiber,which typically has a core radius R_(core) of a few micrometers (μm),the z-averaged modulus Δn(x,y) of the refractive index perturbationsΔn(x,y,z) in this example is:

$\begin{matrix}{{{\overset{\_}{\Delta\; n}( {x,y} )}:={{\frac{1}{L}{\int_{0}^{L}{{{\Delta\;{n( {x,y,z} )}}}{dz}}}} = {1.2 \cdot 10^{- 7}}}},{{x^{2} + y^{2}} \leq {R_{core}^{2}.}}} & (15)\end{matrix}$with a sufficient variation in the local shape and curvature ofΔn_(z)(z) to attain an average reflection of −57 dB per 20 cm (−80dB/mm=−20 dB/km) in the wavelength (λ) range (in-band) of approximately1550±7.5 nm. In this calculation, we assume a coupling coefficient withmodulus |μ_(LP) ₀₁ _(,LP) ₀₁ |≈1 in Eq. (5). To achieve the samereflectivity with fiber modes that have smaller coupling coefficientsμ_(p,r), Δn needs to be increased inversely proportional to |μ_(p,r)|.

The expected level of −80 dB/mm can be observed for a wide range ofintegration lengths, from l=1 mm (in FIGS. 1A and 1B) to l=30 mm (inFIGS. 2A and 2B). As people skilled in the art will appreciate, thismeans that the backscatter from Δn(x,y,z) in Eq. (2) adds incoherently,as in the case of native Rayleigh scattering. Since −80 dB/mm is thesame as −20 dB/km, a total length of approximately L=1 km is possible inthis case without violating the above-mentioned condition that the totalbackscattering level should be below −20 dB to avoid MPI.

As FIGS. 1A and 1B show, a spatial resolution of approximately 1 mm ispossible with such 20 cm-long individual sections of 15 nm bandwidth,because R_(LP) _(01→) _(LP) ₀₁ (λ,z) does not significantly drop belowthe design level of −80 dB/mm within the wavelength band of interest,i.e., 1550±7.5 nm, for any length that is significantly longer than theintegration length l=1 mm. In general, we define the in-bandreflectivity enhancement factor β_(in-band)>0 as the ratio of totalbackscatter R_(p→r) ^((fiber)) to Rayleigh backscatter R_(p→r)^((Rayleigh)) according to:

$\begin{matrix}{{\gamma_{i\; n\text{-}{band}}( {z,l} )}:=\frac{R_{p->r}^{({fiber})}( {\lambda_{i\; n\text{-}{band}},z,l} )}{R_{p->r}^{({Rayleigh})}( {\lambda_{i\; n\text{-}{band}},z} )}} & (16)\end{matrix}$in the bandwidth of high scattering. In the example of FIGS. 1A and 1B,we have |λ_(in-band)−1550 nml≤7.5 nm, and assuming a standard singlemode fiber with the typical Rayleigh scattering level R_(p→r)^((Rayleigh))=−102 dB/mm, we have in-band values of R_(p→r)^((fiber))(λ_(in-band))≈R_(p→r)(λ_(in-band)). and λ_(in-band)≈22 dB. Torelate the in-band and potentially unwanted out-of-band enhancement, wedefine the out-of-band reflectivity suppression factor δ_(out-of-band)>1according to

$\begin{matrix}{{\delta_{{out}\text{-}{of}\text{-}{band}}( {z,l} )}:={\frac{R_{p->r}^{({fiber})}( {\lambda_{i\; n\text{-}{band}},z,l} )}{R_{p->r}^{({fiber})}( {\lambda_{{out}\text{-}{of}\text{-}{band}},z,l} )}.}} & (17)\end{matrix}$In the example of FIGS. 1A and 1B, we have |λ_(out-of-band)−1550 nm|>7.5nm, R_(p→r) ^((fiber))(λ_(out-of-band))≈R_(p→r)^((Rayleigh))(λ_(out-of-band)) and λ_(out-of-band)≈22 bB. The spatialindex perturbation is reproducible along the fiber length to achieve atotal sensor length that far exceeds 119.5 cm. At this moderate level ofbackscatter, longer sensors in which the sensor length exceeds one (1)kilometer (km) are possible without significant MPI.

The setup for FIGS. 3A, 3B, 4A, and 4B includes twelve (12) individual25 mm-long sections with an overlap of 0.5 mm between each section,thereby resulting in a 29.4 cm-long fiber. To achieve the intendedbackscatter enhancement, the refractive index perturbation Δn_(z)(z)(see Eq. (3)) does not need to be periodic or quasi-periodic with thisperiod of 25 mm or 24.5 mm, respectively. The average refractive indexperturbations in the core of the fiber had an average amplitude of

$\begin{matrix}{{{\overset{\_}{\Delta\; n}( {x,y} )}:={{\frac{1}{L}{\int_{0}^{L}{{{\Delta\;{n( {x,y,z} )}}}{dz}}}} = {1.2 \cdot 10^{- 6}}}},{{x^{2} + y^{2}} \leq R_{core}^{2}},} & (18)\end{matrix}$with a sufficient variation in their local shape and curvature to attainan average reflection of −46 dB per 25 mm (≈−60 dB·(1/mm)≈−30 dB/m) inthe same in-band range as in FIGS. 1A, 1B, 2A, and 2B. As FIGS. 3A and3B show, a sub-mm resolution is possible with such 25 mm-long individualsections of 15 nm bandwidth, because R_(LP) ₀₁ _(→LP) ₀₁ (λ,z) does notdrop significantly below the design level of −60 dB/mm within thewavelength band of interest, i.e., 1550±7.5 nm, for any length that issignificantly longer than the integration length l=0.3 mm.

A coarser spatial resolution loosens the above criterion for blind spotsalong the fiber, see FIG. 2 in comparison to FIG. 1, and see also FIG. 4in comparison to FIG. 3. Also, those having skill in the art willappreciate that longer design lengths for individual lengths that makeup the overall grating may be preferable for fabrication.

The disclosed embodiments enjoy numerous advantages as compared to otherapproaches. For example, many fibers are constrained by specificationsother than the requirement of high backscattering. For instance, whileit is possible to increase backscattering by increasing the numericalaperture (NA) or increasing Germanium (Ge) doping in a fiber, anincrease in Ge doping or an increase in NA results in an optical fiberthat typically cannot be optimized for other uses. For instance, a highNA fiber that is still single mode at the signal wavelengths exhibits arelatively high coupling loss, whether by mechanical connector or fusionsplice, as compared to a low NA fiber, such as standard single-modefiber used in telecommunications systems. Use of co-dopants to depressthe NA of a high backscattering fiber is somewhat ineffective forimproving splice and connector loss. Additionally, high NA fibersexperience a relatively high transmission loss. Because transmissionloss is directly related to the increased backscattering resulting fromhigh NA, there are strict limits on the achievable loss level of such anincreased-dopant fiber.

Conversely, the high backscattering fiber disclosed herein increasesbackscattering without substantially increasing the transmission loss orcoupling loss. For instance, the index perturbations that cause thebackscattering in FIGS. 1A through 4B can be introduced into low losstransmission fibers with mode fields and NA matched to standardsingle-mode fiber, thus resulting in high backscattering loss whileproviding low coupling loss and low transmission loss. The resultingfiber would exhibit transmission loss only due to the increasedbackscattering and only over a designated range of wavelengths.

Additionally, reduced coupling loss and transmission loss accompanied byhigh backscattering may be applied to fibers with other properties. Forexample, some fibers have specifically designed linear and nonlinearproperties, such as very low or very high nonlinearity, or very low orvery high group velocity dispersion.

In the disclosed high backscattering fibers, these parameters can bespecifically tuned while at the same time providing a highbackscattering signal. For instance, it is well known that changing themode effective area of a single mode fiber is a way to tune thenonlinearity of the propagation. Thus, a high nonlinearity may beachieved with a reduced mode field area, and conversely, an increasedmode effective area will decrease the nonlinearity of propagation.Increased nonlinearity would benefit applications that require enhancednonlinear effects or gain from Raman, Brillouin, or parametric effects.Decreased nonlinearity would benefit applications that requirepropagation without nonlinear distortion.

For some embodiments, axial variation of backscatter can be introducedalong a fiber. For example, backscatter can be made stronger at thedistal end of the fiber, thereby counteracting the natural attenuationof the signal during propagation. The disclosed high backscatter fibercan also control the optical bandwidth of backscatter, levels oftransmission loss, coupling loss, splice loss, connector loss, and modefield area. Furthermore, the disclosed high backscatter fiber can alsobe used in conjunction with specific active characteristics, such asoptical gain or nonlinearity, which can be induced, e.g., by rare-earthdopants or Raman gain. Similarly, the disclosed fiber can specificallycontrol dispersion or birefringence and other linear or nonlinearpropagation properties.

Because of the characteristics of backscattering, the disclosed fiberscan also provide controlled, intentional sensitivity to environmentalconditions. For example, temperature, strain, bend, twist, H₂,corrosion, and other sensitivity can be provided by using materials thatare intentionally sensitive to, for example, H₂ darkening. Otherbenefits include the following:

The combination of high back scattering and high precision placement ofa core with respect to other cores or stress rods or the fiber axis andvarious multicore or micro-structured fiber cross sections, includingtwisted and non-twisted fiber can be advantageous for certain types ofsensors. For instance, shape sensing can be achieved in twistedmulticore fiber. For such a fiber to be useful, the multiple cores mustbe placed within the fiber with great accuracy in order to maintain acertain calibration for the optical sensor. Such accurate placementrequires precision machining and consolidation of the preform. If thecores have been designed for high scattering, their thermomechanicalproperties may not be well suited to such precise fabrication. Forinstance, when the Ge content of a silica core is increased, itsRayleigh back scattering will increase. However, such high Ge dopedcores have lower viscosity compared to the surrounding silica,complicating the fabrication. Therefore, a means to increase the backscattering without the requirement of increased Ge content is desirablein order to achieve high precision placement of a core or cores within afiber while still having the possibility of large back scattering.

Center wavelength of operation may have to be constrained for certainapplications, thus requiring scattering for certain wavelengths, but notothers. For example, very long wavelengths or other wavelengths whereRayleigh scattering is dominated by infrared (IR) loss and otherscattering mechanisms. For longer wavelengths in silica fibers,typically above 4 μm, there is increased IR loss. Back scattering fromRayleigh scattering may not be sufficient due to this loss. As a result,sensors that require such long wavelengths will require additional backscattering to be useful. In another example, it may be necessary toallow loss and low back scattering propagation at one wavelength, whilehaving high back scatter at another wavelength. Typical waveguidescannot provide such selective enhancement at a given wavelength or bandof wavelengths. The modifications described herein allow for suchincreased back scattering over a given desired bandwidth.

Fiber lengths that include lasers, cavities or lasing are also used insome applications. Such active waveguide devices can be used for sensingor light generation. In such devices it may be necessary to increaseback scattering in order to improve the lasing properties or in order toprovide a monitoring signal to give information about the lasing devicealong its length.

Fibers in which backscatter intensity scales linearly or at least lessthan quadratically with the length of the fiber are important forcertain sensing applications. It is known that a Rayleigh scatteredoptical signal scales linearly with the length of the waveguide due tothe incoherent nature of the scattering. A fiber with increasedscattering could also be designed to increase back scattering linearlywith the length of waveguide used. Such a simple linear increase wouldfor instance, allow for the enhanced scattering waveguide to be usedwith the same sorts of algorithms that would be used with Rayleighscattering with only an increase in signal to noise ratio beingavailable in the enhanced fiber.

Fibers in which backscatter intensity scales linearly or at least lessthan quadratically with the modulation induced in the fiber are ofinterest for some applications. Thus, the enhanced fibers would besimilar to Rayleigh scattering in standard fibers which exhibit aroughly linear relationship between index modulation and scatteringintensity.

The fibers of this disclosure include additional variations inrefractive index, unlike those that result from thermal fluctuations.These additional variations preferably have some long-range order. Forexample, in part of the cross section where the propagating modeintensity is highest, the index variations (also designated herein asperturbations) will preferably have little-to-no variation in thedirection transverse to the optical fiber. Thus, core guided light willexperience minimal overlap with radiation modes, giving rise to lesstransmission loss and more backscattering. The refractive indexvariations extend, in some embodiments, into the fiber claddingsufficiently to suppress coupling from the core to the cladding modescompletely or almost completely.

Index variations may have a spatial spectrum that is peaked at one ormore length scales. One example of such a length scale would be of theorder of 500 nm. Such a length scale would increase scatter near awavelength of 1550 nm in a typical single-mode fiber without increasingthe scattering at other wavelengths. For some embodiments, the indexvariations would exhibit a primary length scale and would exhibit anon-repeating phase variation about this primary length scale. That is,at any point along the fiber, index variations with the primary lengthscale would be observed. However, the phase and amplitude of theserefractive index variations would be random from one spatial point toanother.

In yet other embodiments, the variations would repeat over some lengthscale much longer than the primary spatial frequency peak, such as, forexample, repeating over a length scale of 1 cm or 2.5 cm, as in FIGS.1A, 1B, 2A, and 2B, with or without gaps or overlaps of the 1 cm or 2.5cm long sections. Alternatively, the pattern can be partially periodic.Thus, the same pattern (or portions of the same periodic pattern) mayappear with varying phase.

In yet other embodiments, the refractive index variations would be largeenough to increase backscattering, but not so large that multiplescattering (multipath interference, MPI) would affect measurements.Thus, the backscatter would be much larger than the backscattering forRayleigh scattering while still occurring only once in the waveguide. Ina preferred embodiment, the backscattering from each point along thefiber waveguide would be the maximum value consistent with therequirements of minimal sensor performance degradation due to MPI. Thatis, if a total backscattering level below −20 dB was required for thesensor interrogator to operate as mentioned above, the singlebackscattering signal at each point would be as large as possiblesubject to the constraint that the impact of multiple backscattering isnegligible in the output signal. It is understood that this optimalscattering might require the backscattering signal to not be uniformalong the fiber.

Alternatively, the induced modulation can be chosen such that it isminimal in amplitude while still obtaining the maximum possible backscattering signal.

In another embodiment, there would be two or more primary length scalesfor the index variations. In yet another embodiment, the backscatteringsignal would vary along the fiber. The backscattering signal might bethe same as the native, inherent scattering for certain points along thefiber.

Some embodiments of the high-scattering optical fiber comprises aRayleigh scattering that is greater than −99 dB/mm and a coupling lossof less than 0.2 dB (preferably, less than 0.1 dB) at a wavelength rangebetween 1450 nm and 1650 nm, preferably between 1500 nm and 1625 nm,when coupled to a G.652-standards compliant optical fiber. Insofar asthose in the optical fiber industry are familiar with the G.652standard, further discussion of G.652 is omitted here.

Some embodiments comprise a high backscattering fiber with abackscattering power that is greater than −99 dB/mm within its operatingwavelength range, and a transmission loss that is less than 10 dB/km,but preferably less than 2 dB/km, within the operating wavelength range.For such embodiments, the high backscattering fiber can further comprisea bandwidth (Δμ), wherein Δμ≥1 nm, and an in-band reflectivityenhancement factor (γ), wherein γ≥10 dB (i.e., 10 log₁₀(γ)=10 decibels(dB)). A preferable in-band center wavelength(λ₀) would be:950 nm<λ₀<1700 nm.More preferably, in the range of:1500 nm<λ₀<1625 nm,the high backscattering fiber would exhibit a Rayleigh backscatter(R_(p→r) ^((Rayleigh))) of:−110 dB/mm<R _(p→r) ^((Rayleigh))(λ₀)<90 dB/mm.

In its broadest sense, some embodiments comprise an optical fiber withan effective index of n_(eff), a numerical aperture of NA, a scatter ofR_(p→r) ^((fiber)), a total transmission loss of α_(fiber), an in-bandrange greater than 1 nm, and a figure of merit (FOM) within the in-bandrange, where FOM>1. As noted above, the FOM is defined as:

${FOM} = {\frac{R_{p->r}^{({fiber})}}{{\alpha_{fiber}( \frac{NA}{2n_{eff}} )}^{2}}.}$

More narrowly, the in-band range where the FOM>1 is preferably betweenapproximately 1500 nm and approximately 1625 nm. Also, for someembodiments in which the FOM>1, the optical fiber comprises a couplingloss that is less than 0.2 dB in the in-band range when coupled to aG.652-standard compliant optical fiber. For other embodiments whereFOM>1, the optical fiber comprises a total backscatter that is greaterthan −99 dB/mm within the in-band range and a transmission loss that isless than 2 dB/km within the in-band range. For yet other embodimentswhere FOM>1, the optical fiber has a length that is greater than 20 cm.Although an FOM>1 is described, it should be appreciated that in someembodiments it is preferable to have FOM>2. For certain applications, itshould be appreciated that a higher level of loss (e.g., 10 dB/km to 500dB/km) can be tolerated.

Although exemplary embodiments have been shown and described, it will beclear to those of ordinary skill in the art that a number of changes,modifications, or alterations to the disclosure as described may bemade. For example, those having skill in the art understand how toinduce index perturbations using tailored actinic radiation, such as UV,gamma, or femtosecond infrared (IR), which are all known methods formodifying refractive indices of silica or other glasses. Those havingskill in the art will also understand that the index perturbations areinducible using an interference pattern from two actinic beams, by usinga phase mask with a tailored modulation of its phase, or by using apoint-by-point system with a tailored modulation of the writing beamintensity along the fiber. The tailored modulations are derivable fromthe intended optical spectrum of the backscatter of the optical fiber,as explained above with reference to the equations and FIGS. 1A through4B. Also, while a counter-propagating mode (r) is described, it shouldbe appreciated that this disclosure is equally applicable toco-propagating modes for which +n_(eff,r) can simply be replaced with−n_(eff,r) in Eq. (5). It should be appreciated that backscattering canbe measured using either OTDR or OFDR techniques. For OFDR,index-matching the rear end of the waveguide or fiber is preferable tominimize measurement errors that are induced by MPI with discretereflections from the rear end. Those having skill in the art willappreciate that the disclosed high backscattering fiber can includepolymers, silicates, silica, fluorides, chalcogenide, etc., and that thestructure of these fibers can be solid or micro-structured, includingphotonic crystal fibers, photonic bandgap fibers, hollow core fibers,etc., or any combinations thereof. For instance, a hollow core fiberthat is filled with a certain gas, fluid, plasma, or another solidmaterial. Also, it should be appreciated that, for some embodiments, thehigh backscattering fibers should have induced modulations that areminimal in amplitude while still obtaining the maximum possiblebackscattering signal. Furthermore, although optical fibers are shown inexample embodiments, it should be appreciated that the highback-scattering is applicable to all waveguides. Lastly, unlessdesignated otherwise, either expressly or by context, light is definedto mean visible light, UV radiation, or IR radiation.

All changes, modifications, and alterations should be seen as beingwithin the scope of the disclosure.

What is claimed is:
 1. An optical fiber having a modified index causedby applying a spatial pattern that creates a refractive indexperturbation, the optical fiber comprising: an effective index ofn_(eff); a numerical aperture of NA; a scatter of R_(p→r) ^((fiber)); atotal transmission loss of α_(fiber); an in-band range greater than onenanometer (1 nm); a center wavelength (λ₀) of the in-band range, wherein950 nm<λ₀<1700 nm; and a figure of merit (FOM) in the in-band range,FOM>1, the FOM being defined as:${FOM} = {\frac{R_{p->r}^{({fiber})}}{{\alpha_{fiber}( \frac{NA}{2n_{eff}} )}^{2}}.}$2. The optical fiber of claim 1, wherein the scatter varies axiallyalong the optical fiber.
 3. The optical fiber of claim 2, furthercomprising a distal end and a proximal end, the scatter being strongerat a portion of the distal end than at a portion of the proximal end. 4.The optical fiber of claim 1, wherein 1500 nm<λ₀<1625 nm.
 5. The opticalfiber of claim 1, wherein the scatter comprises a backscatter that isgreater than Rayleigh scattering.
 6. The optical fiber of claim 1,wherein the scatter comprises a backscatter that is more than threedecibels (3 dB) above Rayleigh scattering.
 7. The optical fiber of claim1, wherein the optical fiber exhibits a total backscattering level below−20 dB.
 8. The optical fiber of claim 1, further comprising a modeeffective area that is no smaller than that of a standard single-modefiber.
 9. The optical fiber of claim 1, further comprising a couplingloss of less than 0.5 decibels (dB) when coupled to a transmissionfiber.
 10. The optical fiber of claim 1, wherein the optical fiber is amulticore optical fiber.
 11. An optical fiber having a modified indexcaused by applying a spatial pattern that creates a refractive indexperturbation, the optical fiber comprising: an effective index ofn_(eff); a numerical aperture of NA; a scatter of R_(p→r) ^((fiber))that varies axially along the optical fiber; a total transmission lossof α_(fiber); an in-band range greater than one nanometer (1 nm); and afigure of merit (FOM) in the in-band range, FOM>1, the FOM being definedas:${FOM} = {\frac{R_{p->r}^{({fiber})}}{{\alpha_{fiber}( \frac{NA}{2n_{eff}} )}^{2}}.}$12. The optical fiber of claim 11, further comprising a distal end and aproximal end, the scatter being stronger at a portion of the distal endthan at a portion of the proximal end.
 13. The optical fiber of claim11, further comprising a center wavelength (λ₀) of the in-band range,wherein 950 nm<λ₀<1700 nm.
 14. The optical fiber of claim 13, wherein1500 nm<λ₀<1625 nm.
 15. The optical fiber of claim 11, wherein thescatter comprises a backscatter that is greater than Rayleighscattering.
 16. The optical fiber of claim 11, wherein the scattercomprises a backscatter that is more than three decibels (3 dB) aboveRayleigh scattering.
 17. The optical fiber of claim 11, wherein theoptical fiber exhibits a total backscattering level below −20 dB. 18.The optical fiber of claim 11, further comprising a mode effective areathat is no smaller than that of a standard single-mode fiber.
 19. Theoptical fiber of claim 11, further comprising a coupling loss of lessthan 0.5 decibels (dB) when coupled to a transmission fiber.
 20. Theoptical fiber of claim 11, wherein the optical fiber is a multicoreoptical fiber.